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Symmetry
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Noether and Space-Time Symmetries in Physics—Volume Ⅱ
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Noether and Space-Time Symmetries in Physics—Volume Ⅱ

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 3750

Special Issue Editors

Prof. Dr. Ugur Camci

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Guest Editor
Department of Chemistry and Physics, Roger Williams University, One Old Ferry Road, Bristol, RI 02809, USA
Interests: cosmology; mathematical physics; general relativity; modified gravity; symmetries; collineations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ashfaque H. Bokhari

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Interests: general relativity; Lorentzian geometry; symmetry methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bobomurat Ahmedov

E-Mail Website
Guest Editor
Laboratory of Theoretical Astrophysics, Ulugh Beg Astronomical Institute, Tashkent 100052, Uzbekistan
Interests: relativistic astrophysics; general relativity; neutron stars and black holes
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry is the most common and important principle that guides the formation of realistic theories in science. The notion of symmetry is fundamental not only in cosmological theories, but also in quantum theory, thermodynamics, statistical physics, etc.

Most of the equations for dynamical systems in physics, such as the field equations of any gravity theory, are a system of non-linear ordinary/partial differential equations and are generally difficult to solve. In order to solve these complicated systems of ordinary/partial differential equations, Noether and space–time symmetries are some of the tools that can be used to find their exact solutions. Symmetries of Lagrangians are of great interest on account of Noether’s theorem, which has been widely used in cosmology and gravity theories. Space–time symmetries, such as isometries and collineations, can reduce the number of unknown functions in space–time metric components. The main aim of this Special Issue is to invite researchers working in theoretical and mathematical physics to submit their work, in which Noether and the space–time symmetry approach are used to find exact solutions for the corresponding equations that represent certain dynamical systems.

In this Special Issue, original research articles, reviews, communications and concept papers are welcome. We look forward to receiving your contributions.

Prof. Dr. Ugur Camci
Prof. Dr. Ashfaque H. Bokhari
Prof. Dr. Bobomurat Ahmedov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • noether symmetry
  • space–time symmetry
  • exact solutions
  • cosmology
  • gravity
  • modified gravity
  • conserved quantity
  • astrophysics solutions

Published Papers (4 papers)

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Research

18 pages, 478 KiB  
Article
A Simple Quantum Picture of the Relativistic Doppler Effect
by Daniel Hodgson, Sara Kanzi and Almut Beige
Symmetry 2024, 16(3), 279; https://doi.org/10.3390/sym16030279 - 28 Feb 2024
Viewed by 783
Abstract
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this [...] Read more.
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames. Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)
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10 pages, 247 KiB  
Article
Wave Surface Symmetry and Petrov Types in General Relativity
by Graham Hall
Symmetry 2024, 16(2), 230; https://doi.org/10.3390/sym16020230 - 14 Feb 2024
Viewed by 516
Abstract
This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M,g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other [...] Read more.
This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M,g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other geometrical features of l and (M,g). It is mainly a review of known material but contains some novelties. For example, the brief discussion of the nature of wave surfaces (when viewed geometrically as wave fronts to a null ray direction) in Wave Surfaces Section is new in the sense that although it appeared in the author’s work by the present author, it has not, to the best of his knowledge, appeared in this form anywhere else. Further, the work on conical symmetry and plane waves are, to the best of the author’s knowledge, original with him from earlier papers and are reviewed here while the work on complete wave surface (sectional curvature-) symmetry is believed to be entirely new. Geometrical use of the sectional curvature function is employed in many places. The consequences of the various symmetry conditions imposed on the collection of all wave surfaces to a null direction spanned by a null vector l are described in terms of l spanning a principal null direction of the Weyl tensor (if non-zero) at the point concerned (in the sense of Petrov and Bel). Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)
23 pages, 381 KiB  
Article
Noether Symmetry Analysis of the Klein–Gordon and Wave Equations in Bianchi I Spacetime
by Ugur Camci
Symmetry 2024, 16(1), 115; https://doi.org/10.3390/sym16010115 - 18 Jan 2024
Cited by 1 | Viewed by 1005
Abstract
We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A [...] Read more.
We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A detailed Noether symmetry analysis of the Klein–Gordon and the wave equations for Bianchi I spacetime is presented, and the corresponding conservation laws are derived. Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)
16 pages, 1418 KiB  
Article
Dynamics of Particles with Electric Charge and Magnetic Dipole Moment near Schwarzschild-MOG Black Hole
by Sardor Murodov, Javlon Rayimbaev, Bobomurat Ahmedov and Abdullo Hakimov
Symmetry 2023, 15(11), 2084; https://doi.org/10.3390/sym15112084 - 19 Nov 2023
Cited by 3 | Viewed by 1003
Abstract
The study of electromagnetic interactions among test particles with electric charges and magnetic dipole moments is of great significance when examining the dynamics of particles within strong gravitational fields surrounding black holes. In this work, we focus on investigating the dynamics of particles [...] Read more.
The study of electromagnetic interactions among test particles with electric charges and magnetic dipole moments is of great significance when examining the dynamics of particles within strong gravitational fields surrounding black holes. In this work, we focus on investigating the dynamics of particles possessing both electric charges and magnetic dipole moments in the spacetime of a Schwarzschild black hole within the framework of modified gravity (MOG), denoted as a Schwarzschild-MOG black hole. Our approach begins by offering a solution to Maxwell’s equations for the angular component of the electromagnetic four potentials within Schwarzschild-MOG spacetime. Subsequently, we derive the equations of motion and establish the effective potential for particles engaged in circular motion. This is achieved using a hybrid formulation of the Hamilton–Jacobi equation, encompassing interactions between electric charges and magnetic dipole moments, the external magnetic field (assumed to be asymptotically uniform), and interactions between the particles and the MOG field. Furthermore, we investigate the impacts of these three types of interactions on critical parameters, including the radius of innermost stable circular orbits (ISCOs), as well as the energy and angular momentum of particles when situated at their respective ISCOs. Finally, a detailed analysis concerning the effects of these interactions on the center-of-mass energy is presented in collisions involving neutral, electrically charged, and magnetized particles. Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)
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